Prove that (1+cosθ)(1−cosθ)=(sin^2)θ

Prove that $$\displaystyle{\left({1}+ \cos{\theta}\right)}{\left({1}- \cos{\theta}\right)}={{\sin}^{2}\theta}$$

• Questions are typically answered in as fast as 30 minutes

Plainmath recommends

• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself.

Macsen Nixon

We have to prove that $$(1+\cosθ)(1−\cosθ)=\sin^2θ$$

Let us start from left hand side. By using the identity $$a^2−b^2=(a+b)(a−b)$$ we get $$(1+\cosθ)(1−\cosθ)=1−\cos^2(θ) =\sin^2θ$$